# Worksheet: Combining Functions

In this worksheet, we will practice adding, subtracting, multiplying, or dividing two given functions to create a new function and identifying the domain of the new function.

Q1:

What is the domain of the quotient , in terms of the domains of and ? Assume that both domains are subsets of the set of real numbers.

• Athe difference between the domain of and the domain of
• Bthe intersection of the domain of and the domain of
• Cthe larger of the domain of and the domain of
• Dthe union of the domain of and the domain of
• Ethe intersection of the domain of and the domain of

Q2:

Determine the common domain of the functions and .

• A
• B
• C
• D
• E

Q3:

If and are two real functions where and , determine the value of if possible.

• A
• B
• Cundefined
• D

Q4:

Find the domain of the function .

• A
• B
• C
• D

Q5:

If and , then find and fully simplify an expression for .

• A
• B
• C
• D

Q6:

If where , and where , find the value of if possible.

• Aundefined
• B46
• C16
• D36

Q7:

Given that , where , and , where , evaluate .

• A
• B
• C724
• D

Q8:

If and are two real functions where and , determine the value of if possible.

• A
• Bundefined
• C1
• D

Q9:

Given that , , and , determine in its simplest form.

• A
• B
• C
• D
• E

Q10:

Given that , , and , simplify the function , and determine its domain.

• A, domain
• B, domain
• C, domain
• D, domain
• E, domain

Q11:

Given that and find and state its domain.

• A,
• B,
• C,
• D,
• E,

Q12:

Given that and find the value of if possible.

• Anot defined
• B0
• C
• D

Q13:

Given that and find and state its domain.

• A,
• B,
• C,
• D,
• E,

Q14:

If and are two real functions where and determine the domain of the function .

• A
• B
• C
• D

Q15:

If and are two real functions where and , find the domain of the function .

• A
• B
• C
• D
• E

Q16:

If where , and where , find and the domain of .

• A,
• B,
• C,
• D,
• E,

Q17:

If where , and where , then find and its domain.

• A,
• B,
• C,
• D,

Q18:

If where , and where , find and fully simplify and determine the domain of .

• A,
• B,
• C,
• D,
• E,

Q19:

If where , and where , find and the domain of .

• A,
• B,
• C,
• D,
• E,

Q20:

If and are two real functions where and , determine the domain of the function .

• A
• B
• C
• D
• E

Q21:

Given that and find and state its domain.

• A,
• B,
• C,
• D,
• E,

Q22:

Given that and find and state its domain.

• A,
• B,
• C,
• D,

Q23:

If and are two real functions where and , find the domain of the function .

• A
• B
• C
• D
• E

Q24:

Given that and are two real functions where and , find the value of if possible.

• A0
• B35
• Cundefined
• D

Q25:

Given that and are two real functions where and , find the value of if possible.

• A
• B3
• C
• Dundefined
• E